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Stage 3 - data – sector graph

Strategy

Students can:

interpret a sector graph

When students read a question that contains a picture, graph, table or diagram they need to read all the information provided and be able to interpret the visual representations that the tables and graphs provide.

At this Stage, students need to collect their own data, create tables and graphs and interpret graphs and tables. It is also vital to expose students to the use of data and graphs in the media and wider community and how they convey meaning and information, sometimes showing a bias or presenting the information in a way to persuade the consumer. This provides an opportunity to discuss how and why scale is used and that it is sometimes used to change how information may be interpreted.

The advantages and disadvantages of different representations of the same data in different graphs should be explicitly taught. Students need to choose an appropriate graph to convey meaning for their information, understanding that some graphs have particular uses e.g. Line graphs should only be used where meaning can be attached to the points on the line between plotted points. Graphs are chosen based on what data is being represented, not based on what the student likes.

Activities to support the strategy

Activity 1 – Interpreting sector graphs

When teaching students how to interpret data from a sector graph, it is important that teachers guide students to consider each of the following:

identify the graph's title which indicates what the graph is about

examine the sectors to identify that each sector represents part of a whole. If the sectors are labelled as percentages the total of all the sectors should add to 100%

consider the sector labels to determine the category of information represented in each sector

use mathematical methods to perform calculations such as combined percentages and to find missing values.

In this activity students will interpret data from a sector graph to make calculations which provide information about the relative size of each Australian state and territory's coastal waters as a percentage of the whole of Australia's marine area.

Order the coloured sectors from smallest to largest. Emphasise that the highest percentage sector represents the largest quantity.

8. Demonstrate how to determine the size of each sector as:

a fraction of the whole

a percentage of the whole

9. Students refer back to the sector graph with equal sectors (quadrants). Use a protractor to measure the angle size of each quadrant (90°).

calculate the angle size at the centre of the circle percentage

90° x 4 = 360°

Using angle size, determine what percentage of the circle is represented by each colour.

10. Repeat step 7 using a different number of lollies (jelly beans/Smarties) such as 5 or 12 or 18 or 54. Discuss graphs.

Further activities

11. Students in pairs, conduct a class survey to collect data on a chosen topic. Record the data in a table.

12. Use the data to construct a sector graph. Use a key to identify each sector. Students demonstrate the relationship between the key and the sectors.

13. Students write their own questions using the graph and key and give to other students to answer.

References

Australian curriculum reference: ACMSP147

Interpret and compare a range of data displays, including side-by-side column graphs for two categorical variables

NSW syllabus reference: MA3-18SP

Uses appropriate methods to collect data and constructs, interprets and evaluates data displays, including dot plots, line graphs and two way tables. MA3-7NA: compares, orders and calculates with fractions, decimals and percentages

NSW literacy continuum reference: REAC11M4

Reading texts, Cluster 11, Marker 4: Manipulates multiple texts that include a variety of purposes and modes to locate information for a specific purpose.

NSW Department of Education

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This information is current as at 26/05/2019 01:06am, AEST. For the most up-to-date information, go to https://education.nsw.gov.au/public-schools/selective-high-schools-and-opportunity-classes/year-7/outcome.